Introduction

Piles are structural members made of timber, concrete, steel or other materials which are used to transmit loads from superstructure to deeper soil strata. These are referred to as deep foundations as the foundation level is much below the depth of shallow foundations (Chapter 4). The definitions, classifications and details of pile foundations are given in Chapter 9. The situations where pile foundations may have to be used are indicated below.

10.2

Use of Pile Foundations

Pile foundations may be used for the following situations: 1. To transfer loads through water or soft soil to a suitable bearing stratum (end bearing or point bearing piles). 2. To transfer loads in a relatively weak soil by means of skin friction along the length of the piles (friction piles). 3. To compact granular soils (thus increasing their bearing capacity) (compaction piles). 4. To carry the foundation beyond the depth of scour to provide safety in the event the soil is eroded away. 5. To anchor down the structures subjected to uplift due to water pressure or excessive moments (tension piles or uplift piles). 6. To provide anchorage against horizontal forces from sheetpiling walls or other pulling forces (anchor piles). 7. To shield water front structures against impact from ships or other floating objects (fender piles and dolphins). 8. To carry large horizontal or inclined loads (batter piles).

10.3

Types of Piles and Pile Groups

Piles may be classified according to their installation, composition or function. The details are given in Chapter 9. Generally piles are used in groups to carry the large loads coming from the Foundation Design: Theory and Practice N. S. V. Kameswara Rao © 2011 John Wiley & Sons (Asia) Pte Ltd. ISBN: 978-0-470-82534-1

Foundation Design

352

Figure 10.1

Pile groups carrying heavy superstructures.

superstructure as shown in Figure 10.1. The group may consist of three or more piles in general, and two piles occasionally. The minimum spacing (center to center) of piles suggested by a few building codes are given in the following Table 10.1 (Bowles, 1996). Table 10.1 Minimum spacing of piles. Type of pile

BOCA, 1993

NBC, 1976

Chicago, 1974

Friction Point bearing

2D or 1:75 H 760 mm 2D or 1:75 H 610 mm

2D or 1:75 H 760 mm 2D or 1:75 H 610 mm

2D or 1:2 H 760 mm

where D: pile diameter; H: diagonal distance for rectangular shaped piles.

Optimum spacing between piles, s, generally recommended for use is 2.5D to 3.5D or 2H to 3H. For pile groups carrying lateral and/or dynamic loads, larger spacing is more efficient. Though maximum spacing between piles is not prescribed in building codes, spacing up to 8D to 10D are used depending on the design and economy.

10.4

Efficiency of Pile Groups

The typical stresses/soil pressures produced from shaft friction or end bearing of a single pile and a group of piles are shown in Figure 10.2. If piles are used in groups, there may be an overlap of stresses, as shown in Figures 10.2(b), (d) and (e), if the spacing is too close. If the overlap is large, the soil may fail in shear or settlement will be very large. Though the overlapping zone of stresses obviously decreases with increased pile spacing, it may not be feasible since the pile cap size becomes too large and hence expensive.

Design of Piles and Pile Groups

Figure 10.2

353

Stresses in soil due to loads on single pile and pile groups.

It is a common practice to calculate the capacity of a pile group by means of an efficiency factor Z given as Z¼

ultimate load capacity of pile group sum of ultimate load capacities of individual piles

ð10:1Þ

Several empirical efficiency formulae are used to relate group efficiency to pile spacings for piles in cohesive soils (Poulos, 1980), as follows: 1. Converse–Labarre formula (Poulos, 1980) h i þ ðm1Þn B ðn1Þm mn Z ¼ 1 90 where B ¼ tan1 ðd=sÞ m ¼ number of columns of piles in the group n ¼ number of rows of piles in the group

ð10:2Þ

Foundation Design

354

d ¼ diameter of the pile s ¼ spacing of the piles in the group. This equation can only be applied to rectangular groups with regular arrangement, that is, m, n and s can be identified. 2. Feld’s rule, which reduces the calculated load capacity of each pile in a pile group by 1/16 for each adjacent pile taking no account of the pile spacing (Ramiah and Chickanagappa, 1981). 3. There is another empirical rule (Iyer, 1995) in which the calculated load capacity of each pile is reduced by a proportion a for each adjacent pile where a¼

1d 8s

ð10:3Þ

where d ¼ diameter of the pile and s ¼ spacing of the piles For pile groups in sands it is fairly well established that the group efficiency may often be greater than 1. The axial capacity of a pile group may be calculated in much the same way as that for a single pile, the only difference being that the failure of the pile group as a block has now to be considered as shown in Figure 10.3 and discussed in subsequent sections.

Figure 10.3 Maximum capacity of pile group.

10.5

Analysis and Design of Pile Foundations

Due to the wide variety of choices of piles based on materials, methods of construction, pile capacity assessment, applications, site conditions and so on, methods of analysis and design also vary in some details but mainly follow the usual laws of mechanics. The usual methods followed are discussed below.

10.5.1 Loads and Pile Configuration The pile group can be designed and analyzed for any number of loads coming on the structure. However, a configuration of the pile group has to be selected (as an initial guess) in accordance with the loads that the pile group has to cater for. This is achieved by a set of heuristics inherent

Design of Piles and Pile Groups

355

in any design process. The first section gives the handling of the loads to make it more amenable for the choice of a pile group, the second section deals with how an initial selection of a pile group is made and the final section deals with the checks imposed on the group and how a final selection is made.

10.5.2 Loads The loads are specified in the form of a point of action of the load, the x, y and z components of the forces and the x, y and z components of the moments. The axis that is chosen by the user to specify the loads is not important since the loads are transformed so that the origin passes through the C.G. of the pile group (C.G. of cross sectional area of piles). There are distinct advantages of transforming the axis so that the origin passes through the C.G. of the pile group (C.G. of cross sectional area of piles). These advantages are listed below. 1. The major advantage of such a transformation is the alignment of the pile group. Once the loads have been so transformed, the pile group can be placed so that the length and breadth of the pile group are in conformity with the spatial distribution of the loads. An alignment in variation to this would result in a pile group spread over an extent that is much more than is required. 2. It is also preferable to make the center of the pile group coincide with the center of the load system to minimize the difference in loads coming on the individual piles in the group. This is very important in order to optimize the piles used. 3. Such a transformation also helps in the competitions. The piles in the group can all be defined with the center of pile group at the origin. A pile group with the right handed Cartesian coordinate system is shown in Figure 10.4. The process of transformation is achieved by first rotating the loads about the origin. The loads are then laterally shifted so that the center of the load system coincides with the origin. In such a case, the loads and moments also have to be suitably transformed. Sometimes due to excessive moments or

Figure 10.4

Pile group subjected to general loads and moments.

Foundation Design

356

excessive differences in the loads, the center of the force system may be very far away from the geometric center of the points of application of the loads. In such a case the center has to be limited to the middle third of the area over which the loads are spread or else the moments coming on the pile cap may become excessive.

10.5.3 Pile Configuration The number of piles can be easily selected on the basis of the axial and lateral loads on the system and the axial and lateral capacities of the piles. There are two criteria which govern the initial selection of the pile configuration: 1. The pile group should be oriented such that the length of the group lies in the direction perpendicular to the axis having a greater moment. Since the piles have now been oriented with respect to the loads, this leaves us to choose only between two perpendicular directions. 2. The pile group should be oriented such that the length of the group lies as far as possible along the length of the load system. On the basis of these two criteria an initial number is assigned according to which we can choose an appropriate length to width ratio of the group.

10.5.4 Checks Imposed on the Pile Group Checks are imposed on the selected pile group in stages. Initially a check for the extent of the load and the pile group is imposed in order to ensure that the loads do not come on the pile cap at a point outside the pile group. This would result in excessive moments in the pile cap. It is assumed that all loads Px, Py, and Pz transmitted from the superstructure are shared by piles in the group in proportion to their areas of cross section. Next, checks are imposed such that the individual piles have adequate factors of safety against axial load, lateral load, moments and combined axial and lateral load. The axial load coming on a pile is calculated by the expression Pz Ai Mx yi Ai My xi Ai Pzi ¼ P Ixx Iyy Ai

ð10:4Þ

where Pzi is the axial load coming on the i-th pile n is number of piles in the group Pz is the resultant of all the vertical loads Mx is the resultant moment about the x axis My is the resultant moment about the y axis. Ai is the area of cross section of the i-th pile. If Ai is the same for all the piles (i ¼ 1 to n) in the group, then PAiA ¼ 1n and the first term on the right hand side (RHS) of Equation (10.4) simplifies i as Pnz . xi,yi are the x, y coordinates of the i-th pile with respect to the origin (C.G. of pile group). x, y, z are the right handed coordinate axes as shown in Figure 10.4. Ixx, Iyy and Izz are the moments of inertia of the pile group about the x, y and z axes respectively. Ixx , Iyy and Izz are obtained as given below (using parallel axes theorem and neglecting the moments of inertia of the pile cross sections about their own axes).

Design of Piles and Pile Groups

357

Ixx ¼ A1 y21 þ A2 y22 þ þ An y2n ¼ Iyy ¼ A1 x21 þ A2 x22 þ þ An x2n ¼ P 2 Izz ¼ Ixx þ Iyy ¼ Ai r i

P P

Ai y2i Ai x2i

ð10:5Þ

where r2i ¼ x2i þ y2i The lateral loads coming on any pile along x and y direction (horizontal axes) can be expressed as Px Ai M z y i Ai ð10:6Þ Phxi ¼ P Izz Ai Py Ai Mz xi Ai Phyi ¼ P þ Izz Ai Thus the resultant horizontal load on the i-th pile is qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ Phi ¼ P2hxi þ P2hyi

ð10:7Þ

ð10:8Þ

where Phxi is the lateral load coming on the i-th pile in the x direction. Phyi is the lateral load coming on the i-th pile in the y direction. Px is the resultant of all the horizontal loads in the x direction. Py is the resultant of all the horizontal loads in the y direction. Mz is the torsional moment about the z axis. xi, yi are the x and y coordinates of the i-th pile with respect to the origin (C.G. of pile group). Ai is the area of the i-th pile. If Ai is the same for all the piles (i ¼ 1 to n) in the group, then Ai / S Ai ¼ 1/n and the first term on the right hand side (RHS) of Equations (10.6) and (10.7) P simplifies as Pnx and ny respectively. Izz is the torsional moment of inertia of the pile group. The safety against combined axial and lateral load can be checked by treating the pile as a column under combined axial and lateral load. After this the pile group is checked for group capacities. Finally a check on the settlements of the individual piles as well as on the pile group is made. It is possible, that after all these checks there are several alternative designs feasible. In order to make a final choice a representative economic analysis is made. Three factors are considered in the economic analysis: 1. The quantity of concrete 2. The quantity of steel 3. Additional costs per unit length of the pile which could be interpreted as the cost of installation of the pile.

10.6

Lateral Capacity of Piles

Deep foundations subjected to lateral loads should be designed so that they satisfy the following conditions (Iyer, 1995):

Foundation Design

358

1. The pile or drilled shaft should be able to carry the imposed load with an adequate margin of safety against failure in bending. 2. The deflection of the foundation under the load should not be larger than the tolerable deflection for the structure it supports. 3. The soil around the pile or shaft should not be loaded so heavily that it reaches its ultimate load carrying capacity.

10.6.1 Single Pile A single pile with the lateral load is shown in Figure 10.5. There are different design philosophies prevalent for the estimation of the lateral load carrying capacity of a single pile.

Figure 10.5

Single pile subjected to lateral/horizontal load.

1. Conventional Statical Approach The simplest method of estimating the ultimate lateral resistance of a floating pile is to consider the statics of the pile by drawing an approximate soil resistance profile along the length of the pile. Brom’s (1964) theory is an application of this approach in which simplifications are made to the ultimate soil resistance distribution along the pile and also full consideration is given to restrained or fixed-headed piles as well as unrestrained or free headed piles. For a general distribution of soil resistance with depth the method given by Brinch Hansen and Christensen (1961), described in detail by Tomlinson (1977), may be used.

Design of Piles and Pile Groups

359

2. Subgrade Reaction Approach This approach is based on the assumption that the soil reaction q is proportional to the deflection of the pile. The ratio of the soil reaction to the deflection is called the modulus of subgrade reaction, ks , which is a function of the modulus of elasticity, Es (further details are given in Chapter 4). Solutions have been developed for Es constant with depth (Hetenyi, 1946) and also for variation of Es with depth and for layered soils. 3. p–y Curves The subgrade reaction approach is only applicable to the deflection of pile within the elastic compression of soil caused by the lateral loading of piles. The p – y curves developed by Reese (Tomlinson, 1977) represent the deformation of the soil at any given depth below the soil surface for a range of horizontally applied pressures from zero to the stage of yielding of the soil in ultimate shear. 4. Characteristic Load Method The characteristic load method described by Duncan, Evans and Ooi (1994), like the p–y curve approach, takes into account the nonlinearity in the soil response to a lateral load. It gives nondimensional characteristic loads and moments as a means of normalizing the soil response. Curves are then given for the estimation of the ratio of applied load to the characteristic load and applied moment to the characteristic moment for different levels of deflections.

10.6.2 Additional Considerations The lateral load carrying capacity of a single pile depends not only on the horizontal modulus of subgrade reaction of the surrounding soil but also on the structural strength of the pile shaft against bending consequent upon application of a lateral load. While considering lateral load of piles, effect of other coexistent loads including the axial load on the pile should be taken into consideration for checking the structural capacity of the shaft. Values of modulus of horizontal subgrade reaction are given for different types of soils in the codes and are given in Tables 10.2 and 10.3. Also the fixity lengths for the various values of the modulus of subgrade reaction are given in the form of graphs in Figures 10.6(a) and (b) (Part 1 of IS: 2911–1984, 1984). Table 10.2

Typical values of nh as defined in Figure 10.6(a). nh (kg/cm3)a

Soil type

Loose sand Medium sand Dense sand Very loose sand under repeated loading

Dry

Submerged

0.26 0.775 2.076 —

0.146 0.526 1.245 0.041

a

kg is in units of force.

The concept of the fixity length of a pile can also be used to calculate the approximate bending moments caused by the lateral loads in piles to avoid the cumbersome calculations of the BEF approach (Section 10.6.4). This fixity length approach is used by several designers and is illustrated in Sections 10.14 and 10.15.

Foundation Design

360

Table 10.3

Typical values of Kh for preloaded clays.

Unconfined compression strength (kg/cm2)a 2–4 10–20 20–40 40 a

Range of values of Kh (kg/cm2)a

Probable values of Kh (kg/cm2)a

7–42 32–65 65–130 —

7.73 48.79 97.73 195.46

kg is in units of force.

Figure 10.6

Fixity length of piles subjected to lateral loads.

Design of Piles and Pile Groups

361

This is an approximate approach which needs to be used with caution after verifying with local practices and codes. From the distribution of shear force and bending moment diagrams shown in Figures 9.8 and 9.9, such a simplification as illustrated in Sections 10.14 and 10.15 appears to be reasonable. However, it should be verified by the BEF approach or other methods. It may be also noted that maximum BM due to lateral loads in piles is used mainly to compute the reinforcement needed in the pile in combination with the vertical load as in a column. It does not affect any other parameters of pile design, once the maximum allowable lateral load of individual pile is decided. Further, the construction agencies have usually their customized procedures to ensure the allowable maximum bending moment in individual piles (both for driven piles as well as cast in situ piles).

10.6.3 Methods of Analysis In most cases consideration of bending moments and deflections govern design, because the ultimate load carrying capacity of the soil is reached only at very large deflections. The statical approach does not consider the load–deflection response. The method of p–y curves requires a great deal of time to develop the input and is highly computer-intensive. The characteristic load method works only for uniform soil conditions, that is, it assumes that the pile is embedded in the same type of soil throughout its length. Hence the method that can be adopted is one based on the beam on elastic foundation approach described by Vlasov and Leontev (1960), Kameswara Rao (1971). The method is explained in detail in Chapters 4 and 5. Since the method suggested by Brinch-Hansen is much more easy to apply for the case of a short pile it may be used in preference to the beam on elastic foundation approach. This method is given in Section 10.6.5.

10.6.4 Beam on Elastic Foundation Approach This approach is discussed in detail in Chapters 4 and 5. However, a brief discussion is presented below with focus on laterally loaded piles. Noting that the axis of the pile is along the z direction as shown in Figure 10.5, the governing equation for a beam on Winkler foundation can be expressed (Chapter 4) by the differential equation (Hetenyi, 1946) as

Ep I p

d4u þ kh u ¼ p dz4

ð10:9Þ

where Ep is the Young’s modulus of the material of the pile Ip is the moment of inertia of the cross-section of the pile u is the lateral/horizontal displacement of the pile p is the load distribution on the pile, that is, external lateral load applied along lateral (x axis) direction kh is the modulus of subgrade reaction in the horizontal direction.

Foundation Design

362

Vesic (1961) analyzed an infinite (horizontal) beam on an elastic foundation and compared the results with those obtained by the use of Winkler’s hypothesis. He concludes that the problem of bending of beams resting on a semi-infinite elastic subgrade can be treated with reasonable accuracy with the use of the concept of a coefficient of subgrade reaction. He has an expression for the value of kh, which can be adopted for piles as sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 1:3 12 Es B4 Es ð10:10Þ kh ¼ B Ep Ip 1n2s where B is the beam width and Es, vs are elastic constants of the soil. Ep Ip are, respectively, the modulus of elasticity and moment of inertia of the cross section of the pile about the axis of bending. The expression for ks in the vertical direction is given in Equation (4.41). The differential equation needs to be used for piles which are subjected to both axial loads and lateral loads as applicable to a beam–column (Hetenyi, 1946), that is, Equation (10.9) needs to be modified to also take into account the axial load. Accordingly, the modified equation is Ep Ip

d 4u d 2u N þ kh u ¼ p dz4 dz2

ð10:11Þ

where N is the axial load on the beam–column/pile which actually varies with depth due to the friction on the surface of the pile. For the case when N ¼ 0, Equation (10.11) reduces to Equation (10.9). For the case when N varies with depth, numerical solutions can be obtained as described in Chapters 6 and 7. For the case when N ¼ 0, exact or numerical solutions can be obtained using methods discussed in Chapters 5–7. For the case when N ¼ constant again exact solutions can be obtained by the methods described in Chapter 5 (including the method of initial parameters). However for the case when N ¼ constant, initial steps for obtaining the exact solutions as described in Chapter 5 are presented below. The characteristic equation of the ODE that is, Equation (10.11) is Ep Ip m4 Nm2 þ kh ¼ 0

ð10:12Þ

The roots of characteristic equation are

where

in which

m1;2;3;4 ¼ ða ibÞ

ð10:13Þ

sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ N a ¼ l2 þ 4Ep Ip

ð10:14Þ

sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ N b ¼ l2 4Ep Ip

ð10:15Þ

rﬃﬃﬃﬃﬃﬃﬃﬃ kh 4 l¼ 4EI

Design of Piles and Pile Groups

363

Hence the homogeneous solution for Equation (10.11) can be written as uh ¼ C1 F1 þ C2 F2 þ C3 F3 þ C4 F4 ¼ CT F ¼ F T C

ð10:16Þ

C is the matrix of constant coefficients which have to be solved from the boundary conditions. C can be expressed in a matrix form as 8 9 C1 > > > = < > C2 C¼ C > > > ; : 3> C4 F is the basis of solution and is given by 9 8 9 8 az F1 > > e cos bz > > > > > > > = > = < eaz cos bz > 2 ¼ F¼ az > > > > > > > > > F3 > > e sin bz > ; ; : : az e sin bz F4

ð10:17Þ

The derivative of the basis of solutions for the homogeneous solution can be expressed as dfFg ¼ ½NH fF g dz where NH is given by

2

a

60 6 NH ¼ 6 4b

ð10:18Þ 3

0

b

a

0

0

a

b 7 7 7 0 5

b

0

a

0

0

ð10:19Þ

The parameters, that is, displacement u, slope u0 , moment Mb and shear force Q at any point can be expressed as 8 þ u > > > > > > > < u0

u ¼ fCgT fFg u0 ¼

du ¼ fCgT ½NH Fg dz

d 2u Mb ¼ EI 2 ¼ Ef If fCgT ½NH 2 Fg dz Q ¼ EI Hence

d 3u ¼ Ef If fCgT ½NH 3 Fg dz3 9 8 u > > > = < 0 > u ¼ ½Bz¼0 fCg > > > Mb > ; : Q z¼0

or

9 > > > > > > > =

> > > Mb > > > > > > > > > > > ; : Q

¼ BC

(10.20)

ð10:20Þ

ð10:21Þ

Foundation Design

364

If we refer to the matrix on the left of the equality as {Ip}, the matrix of initial parameters, we can write fIp g ¼ ½Bz¼0 fCg ¼ ½AfCg

ð10:22Þ

Hence the {C} matrix can be written as fCg ¼ ½A1 fIp g ¼ ½GfIp g

ð10:23Þ

From Equations (10.20), we get fIp g ¼ ½BfCg ¼ ½B½GfIp g ¼ ½KfIp g

ð10:24Þ

The total solution can be given by u T ¼ uh þ up where uh and up are the homogenous solution and particular integral. The details of obtaining the total solution from now on will be the same as given in Chapter 5. Equations (10.20)–(10.24) are similar to Equations (5.35)–(5.39) in Chapter 5, except that the basis of solutions F1 to F4 (Equation (10.17)), the coordinate axes and the direction of the displacement are different. The general solutions can be obtained as given in Section 5.5. For example, if the parameters at any point (say z ¼ l) are represented as {Fp}, they can be written as fFp g ¼ ½KfIp gfFpart g

ð10:25Þ

where {Fpart} is the matrix of functions depending on the external load. These can be obtained by multiplying the relevant terms of the [K] matrix by the force applied. For the case of a lateral load at the head of the pile the terms of the {Fpart} can be obtained as Fu ¼ Px ðK1;4 Þ Fu0 ¼ Px ðK2;4 Þ FM ¼ Px ðK3;4 Þ FQ ¼ Px ðK4;4 Þ

ð10:26Þ

where Px is the lateral force applied at the head of the pile. For a layered soil profile one could proceed down the length of the pile by expressing the final parameters, at the bottom of the layer, in terms of the initial parameters, at the top of the layer, and considering these final parameters as the initial parameters for the subsequent layer. Proceeding in this fashion one could express the parameters at the bottom of the pile in terms of the parameters at the top of the pile. 10.6.4.1 Infinitely Long Beam For a pile with a lateral load applied at its head, the deflection and slope, tend to zero with increasing depth as is for a beam with a concentrated load as we move away from the point of application of the load. Hetenyi (1946) has found that this distance can be expressed as 1:5p=l. Hence if we were to consider a pile with length greater than 1:5p=l as a infinitely long pile, we could determine the parameters at the top of the pile. Once these have been determined, we could proceed from top to bottom and calculate the lateral carrying capacity as the sum of the soil reaction over the length given by (khu) from top to bottom.

Design of Piles and Pile Groups

365

10.6.5 Short Piles – Brinch Hansen’s Method For short piles Brinch Hansen (Brinch Hansen and Christensen (1961)) suggested a simple method for calculating the lateral load capacity as shown in Figure 10.7. The resistance of the pile to rotation about the point x in Figure 10.7 is given by the sum of the moments of the soil resistance above and below this point. The passive resistance diagram is divided into a convenient number of n horizontal elements of depth L/n. The unit passive resistance of an element at depth z below the ground surface is then given by pz ¼ poz Kqz þ cKcz

ð10:27Þ

where poz is the effective overburden pressure at depth z, c is the cohesion of the soil at depth z, and Kqz and Kcz are the passive earth pressure coefficients for the frictional and cohesive components respectively at depth z (Figure 10.8).

Figure 10.7 Brinch-Hansen’s method for short piles.

The total passive resistance on each horizontal element is pz(L/n)B and by taking the moments about the point of application of the horizontal load, we get X

M¼

z¼x X

z¼l X L L pz ðe þ zÞB pz ðe þ zÞB n n z¼x z¼0

ð10:28Þ

where B is the width/diameter of the pile cross section. P The point of rotation has to be obtained by trial and error and it is correctly obtained when M ¼ 0. Having obtained the center of rotation from Equation (10.28), the ultimate lateral resistance of the pile to the horizontal force

Foundation Design

366

Figure 10.8

Brinch-Hansen’s coefficients Kq and Kc.

Hu can be obtained by taking moments about the point of rotation, that is x xX þL X L L Hu ðe þ zÞ ¼ pz Bðx þ zÞ þ pz BðzxÞ n n x 0

ð10:29Þ

The ultimate bending moment, which occurs at the point of zero shear, should not exceed the ultimate moment of resistance Mu of the pile shaft. However it is quite often found that Mu is exceeded. For cases where this does take place the ultimate lateral load carrying capacity is calculated on the basis of a scheme suggested by Carter and Kulhawy which is reported by Randolph (1981) and Randolph et al. (1992).

10.6.6 Structural Checks It has to be checked that the solution obtained does not violate either the maximum deflection criterion, the limiting moment criterion or the maximum permissible shear force criterion. The maximum permissible lateral deflection of the pile would depend on the use to which the superstructure is to be put and hence is user-defined criterion. The maximum moment of a pile section can be calculated from the shape, dimensions and quantity of reinforcement steel in the pile section by the limit state theory. The minimum quantity of steel to be used as longitudinal reinforcement for bored piles is given as 0.4% of the cross-sectional area of the pile or as required to cater for handling stresses (Part 1 of IS: 2911–1984, 1984). The minimum quantity of steel to be used as longitudinal reinforcement in a driven pile is given as (IS: 2911–1984, Part 1, Section 3) as follows: 1. For piles of length 40 the least width – 2.0%.

Design of Piles and Pile Groups

10.7

367

Pile Group

In the estimation of the lateral load capacity of a pile group an approach similar to that adopted for the calculation of vertical load capacity can be taken. The group capacity of a group of piles is the smaller of the following two values, that is: 1. n times the lateral load capacity of a single pile. 2. The lateral load capacity of an equivalent single block containing the piles in the group and the soil in between them.

10.7.1 Methods Available The concept of efficiency factor for lateral loading, like one for vertical loading, has been suggested by Poulos (1980). He has attempted to plot curves of group efficiency versus spacing/ pile diameter. Instead, Randolph et al. (1992) suggested (avoiding calculations based on efficiency factors) a method taking into account the shear stresses developed on the soil between two piles as shown in Figure 10.9. They gave the expression Pu ¼ 2Ks0 v s tan f0

ð10:30Þ

where K ¼ earth pressure coefficient s0 v ¼ effective vertical stress f0 ¼ angle of internal friction s ¼ spacing between piles. However, they state that the value of K to be used in the above expression is open to question.

Figure 10.9

10.8

Plan view of block failure of piles under lateral load.

Settlement of Piles

The settlement of a pile is the sum of the immediate or elastic settlement and long-term or consolidation settlement. Only the immediate or elastic settlement of the pile/pile group is

368

Foundation Design

discussed in this section along with discussion on the implications of soil pile interaction. The evaluation of primary consolidation settlement of pile groups is discussed in detail in Sections 9.8 and 9.9. The total settlement of a single pile under axial load consists of the following components: 1. Elastic compression of the pile 2. Movement of pile relative to the surrounding soil 3. Settlement of surrounding soil due to pile load; this comprises of elastic deformation and consolidation settlement 4. Settlement of soil under the pile tip (elastic as well as consolidation) 5. Creep of pile material under constant axial load. The settlement of a pile group is more complex because of overlapping of stresses in the soil introduced by the closely spaced piles. Under equal axial load per pile, the pile group generally settles more than a single pile due to the stress overlapping (Figure 10.2). The procedures for settlement analysis varies with the type of piles and the soil conditions, as discussed below.

10.8.1 Point-Bearing Piles on Bedrock If the pile tips are on the rock and if the rock is not soft, the net settlement of a pile is generally not more than a few millimeters after deduction of rebound. However, well designed and constructed buildings supported on piles driven to solid hard rock have been subjected to total settlements several times as much as the net settlement of the test pile. The larger settlements are thought to be the result of one or more of the following factors: 1. 2. 3. 4.

Small uplift of piles due to driving of adjacent piles Long-term creep of pile material under constant load Overlapping of stresses in soil Negative skin friction as a result of disturbance of clay due to pile driving.

However, the total net settlement of well designed and constructed pile foundations on rock generally will not be so large as to cause concern, unless the bedrock is soft. In this case, quantitative analysis is very difficult and in practice it can only be estimated by judging from the characteristics of the rock core samples and local experience, if available.

10.8.2 Point-Bearing Piles in Sand and Gravel The settlement of a single pile driven in granular soils can be readily determined by load test since the settlements of such soils take place immediately after load application. However, the test must be so made to differentiate or eliminate the skin friction. The settlement of a pile group is considerably greater than that of a single point-bearing pile as discussed above. For a group of piles having the customary pile spacing, the tentative relationship shown in Figure 10.10 may be used. Pile groups closely located should be considered as one large cluster if they are connected to different pile caps.

Design of Piles and Pile Groups

369

Figure 10.10 Settlement of group of point-bearing piles in sand. (Reproduced from Proceedings of the 3rd International Conference on Soil Mechanics and Foundation Engineering, vol. 3, A.W. Skempton, “Discussion: settlement of pile group in sand,” p. 172, August 16–27, Ó 1953, Z€ urich, Switzerland, with permission from Geotechnik Schweiz, formerly SGBF Swiss Society for Soil and Rock Mechanics.)

Also, there could be the possibility of additional settlement due to layer or layers of weak soil below the compact or hard layer which supports the pile caps. The stress in lower layers may be approximated by the 60 distribution method as discussed in Section 9.8.

10.8.3 Point-Bearing Piles on Hard Clay Settlement of a single pile or a group of piles driven to hard clay cannot be determined by practical means. A very rough idea as to the order of magnitude of settlement may be obtained by laboratory tests on the basis of broad assumptions, approximations, and simplifications. Records of existing pile foundations are the most valuable information, if available. Load tests on such piles usually give optimistic results because an extremely long time is necessary for consolidation. The process of consolidation may be accelerated if the tip of the test pile is provided with porous material and the excess water is drained out during the test. Even so, a load test may require long time for complete consolidation. Such lengthy load test is not feasible in all construction projects. Therefore, if pile load tests are conducted for the purpose of determining the ultimate bearing capacity, the load settlement relationship as established by the tests must be interpreted very carefully.

10.8.4 Friction Piles in Sand and Gravel The load–settlement relationship of a single friction pile in granular soils can be determined reliably by pile load test. The time required for the test is relatively brief since settlement in such soils takes place shortly after load application. If the settlement of the test pile is acceptable, the settlement of a pile group in such soils will be of no concern. This is because the granular soil between the piles is compacted by displacement of the piles and becomes locked in between as a dense mass. The settlement

370

Foundation Design

probably approaches that of a pier foundation having a depth and base area equal to those of the pile group.

10.8.5 Friction/Adhesion Piles in Clays The settlement of a single friction pile in clay cannot be determined within a short period because of the long time taken for consolidation. With elaborate laboratory tests, the settlement may be computed by elastic theory (Seed and Reese, 1957). There is no accurate method for determination of settlement of friction piles in clays. In practice an approximate settlement analysis may be made by the aid of consolidation on the assumption that the clay is subjected to vertical stresses determined by the methods given in Sections 9.8 and 9.9. Driving piles in clay considerably effects the engineering properties of the clay. The pile driving operation disturbs the clay surrounding each pile, several centimeters thick around the pile surface. The clay in this zone loses a part of its strength due to disturbance. Immediately the disturbed clay begins to loose water due to the stresses setup by volume displacement. If the clay in this disturbed zone is very sensitive, it may lose a large part of its strength and becomes unable even to support the soil above. Hence, it begins to consolidate under its own weight. The strength is usually regained very rapidly as a result of water expulsion. Some 90% or more of its original undisturbed strength may be regained. Eventually the clay in the disturbed zone may become stronger than the original soil. In practice the full load is never applied until several months after pile driving, and hence, the damage due to driving disturbance does not affect the useful strength of the soil. However there are doubtful cases where the clay may not regain its full strength or may not regain it rapidly enough. In either case, laboratory tests of the undisturbed and disturbed samples need to be conducted and analyzed.

10.8.6 Settlement Under Axial Load – Single Pile The existing methods of analysis can be broadly categorized as given below (Poulos, 1980): 1. The load transfer method developed by Coyle and Reese (1966), uses relationships between pile resistance and pile movement measured at various points along the pile. In this method the pile is divided into a finite number of segments. Assuming a tip movement, the movement of the pile segment at midheight is estimated from load transfer/shear strength versus pile movement curves and the elastic deformation equation in an iterative manner. Thus one proceeds up the length of the pile to obtain the load and displacement of the pile head. From a series of such calculations load–settlement curves can be plotted. 2. Analyses based on elastic theory have been carried out by many investigators, such as Butterfield and Banerjee (1971), Randolph and Wroth (1978), and Poulos and Davis (1980). In these analyses the pile is divided into a number of uniformly loaded elements and a solution is obtained by imposing the compatibility constraints between the displacement of the soil and the pile. The displacements of the pile are obtained by considering the compressibility of the pile under axial loading and the soil displacements in most cases are obtained by using Mindlin’s equations for the displacement of a soil mass caused by a loading within the mass.

Design of Piles and Pile Groups

371

3. Finite element solutions have been described by Ellison et al., Desai, Lee and Balaam et al., among others (Iyer, 1995).

10.8.7 Settlement Under Axial Load – Pile Group The settlement of a pile group is the sum of the immediate or elastic settlement ri and the longterm or consolidation settlement rc . The general equation for the calculating ri for a flexible foundation at the ground surface level (discussed in Chapters 3 and 4) is 1n2 ri ¼ qn 2B ð10:31Þ If Eu where ri is the settlement at the center of the flexible loaded area qn is the net foundation pressure B is the width of an equivalent flexible raft n is the Poisson’s ratio If is an influence factor Eu is the deformation modulus for the undrained loading conditions.

10.8.8 Methods of Computation It can be seen from Equation (10.31) that the values of If depends on the ratios H/B and L/B of the pile group, where H ¼ depth of the compressible soil layer, B ¼ width of the pile group, L ¼ length of the pile group. However, it may be more convenient to use the expression given by Janbu, Bjerrum and Kjaernsli (Tomlinson, 1977) to obtain the average immediate settlement of a foundation at depth D below the surface where the equivalent raft foundation is to be located. The base of the equivalent raft for different cases of soil conditions is as shown in Figures 10.11 and 10.12. In layered soils with different values of the deformation modulus Eu in each layer, the strata below the base of the equivalent raft are divided into a number of representative horizontal layers and an average value of Eu is assigned to each layer as shown in Figure 10.13. The dimensions L and B in Figure 10.13 are determined on the assumption that the load is spread to the surface of each layer at an angle of 30 from the edges of the equivalent raft. The total settlement of the pile foundation is then the sum of the average settlements

Figure 10.11

Base of equivalent raft in sandy soils for pile groups.

Foundation Design

372

Figure 10.12

Base of equivalent raft for soft soils.

Figure 10.13 Load distribution beneath pile group in layered soils.

Figure 10.14

Interaction factors for floating piles, L/d ¼ 10.

Design of Piles and Pile Groups

Figure 10.15

373

Interaction factors for floating piles, L/d ¼ 25.

calculated for each soil layer from Equation (10.31). The computation of the settlement of a group of piles is often done by the application of influence factors. There are many such influence factors in literature given by Skempton, Pitchumani and D’Appolonia, Poulos, Randolph and Wroth (Iyer, 1995). Influence factors (aF) were obtained by Poulos by the integration of the Mindlin’s equation for the vertical displacement in a semi-infinite mass resulting from an interior vertical loading and are given in Poulos and Davis (1980). These are given in Figures 10.14–10.17 for various L/d and s/d ratios where L ¼ length of the pile, d ¼ diameter of pile and s ¼ spacing of the piles. The charts are given for different values of soil stiffness K at a value of Poisson’s ratio of the soil ns ¼ 0:5. In these figures, K ¼ ðEp Ip Þ=ðEs L4 Þ where Ep Ip ¼ flexural rigidity of the pile Es ¼ modulus of elasticity of soil L ¼ embedded length of pile.

Figure 10.16

Interaction factors for floating piles, L/d ¼ 50.

Foundation Design

374

Figure 10.17

Interaction factors for floating piles, L/d ¼ 100.

Since these values are obtained for a load acting in a semi-infinite media, curves for correction factor Nh for the effect of finite layer are given in Figure 10.18.

Figure 10.18

Correction factor Nh to interaction factors for the effect of finite layer depth.

Also, since these curves are plotted for a Poisson’s ratio of 0.5, curves for correction factor Nv for the effect of Poisson’s ratio are given in Figure 10.19.

Design of Piles and Pile Groups

375

Figure 10.19 Correction factor Nv to interaction factors for the effect of Poisson’s ratio.

10.9

Settlement Under Lateral Load

The lateral load capacity of the pile can be computed by the beam on elastic foundation approach on the basis of the permissible lateral deflections, as discussed in Section 10.6.4.

10.10

Design of Pile Caps

Pile caps are almost invariably made of reinforced concrete and are designed as individual footings subjected to the column loads plus the weight of the pile cap and the soil above the cap. Under a concentric load, all piles in the same group are assumed to take equal axial loads. Theory, model tests, and field measurements have proved that piles in one group do not take equal loads. Instead, the center piles take less than the outer piles and the corner piles are subjected to maximum loads. The soil under the pile cap is not assumed to offer any support. Wherever the conditions permit, the piles should be arranged in the most compact geometric form in order to keep the stresses in the pile cap to the minimum (Teng, 1964). The criteria for the structural design of the pile caps are illustrated in Figure 10.20. Under an eccentric loading or a concentric loading plus a moment, the pile cap is designed in accordance with the following assumptions: 1. Pile cap is perfectly rigid. 2. Pile heads are hinged to the pile cap; therefore, no bending moment is transmitted from pile cap to piles. 3. Piles are short, elastic columns. Therefore, deformations and stress distribution are planar. These assumptions permit the use of elastic theory for calculation of the pile loads and the stresses in the pile cap, as explained in Section 10.5.

Foundation Design

376

Figure 10.20

Critical sections for the design of pile cap.

Pile caps, similar to spread footings, may have pedestals, stepped or sloping tops. One cap may also support more than two columns. Pile caps should be large enough to have a minimum edge distance of 100–150 mm of concrete beyond the outside face of the exterior piles. In difficult driving conditions where the actual locations of piles may deviate considerably from the required, the edge distance should be increased to provide for such field variations. Ordinarily the piles are embedded at least 150 mm into the cap and the reinforcing bars are placed at a clear distance of 75 mm above the pile head. Therefore the effective depth d of a pile cap is generally about 250 mm less than the total depth d of the pile cap.

10.11

Uplift

When piles are required to resist uplift force in excess of the dead load of the structure, the following steps must be taken: 1. The piles must be anchored sufficiently into the cap, the cap tied to the column and the cap designed for the uplift stresses.

Design of Piles and Pile Groups

377

2. Concrete piles must be reinforced with longitudinal steel for the full net uplift. Splices in all types of piles should be designed for the full uplift. 3. Uplift resistance of a pile is not necessarily a function of its bearing capacity under compression. For friction piles in soft clay, the capacities against compression and uplift are about equal. A friction pile in granular soils may not have an uplift resistance approaching its bearing capacity. Except for friction piles in soft clays, the uplift capacity of the pile must be determined by pull out tests. When large uplift forces are anticipated, pedestal type piles may be beneficial. The total uplift resistance of a pile group is calculated as the smaller of the following two values: 1. Uplift resistance of a single pile number of piles in the group. 2. Uplift resistance of the entire group as a block (Figure 10.21).

Figure 10.21

10.12

Uplift capacity of pile group.

Batter Piles

When piles are subjected to excessive lateral loads, it might be more economical and desirable to provide batter piles. Common batter varies from 1 horizontal:12 vertical to 5 horizontal:12 vertical. When batter exceeds 3 horizontal:12 vertical, special driving equipment is necessary and hence may be very costly. The usual assumption in the design of batter piles is that the pile is capable of resisting the same axial load as a vertical pile of the same type and size and driven to the same stratum. There are several methods for analysis of pile foundations involving batter piles. Some of these are given below: 1. The most conservative method is one that provides enough batter piles to resist all the horizontal force. The capacity of a batter pile in resisting a horizontal force is assumed, in

Foundation Design

378

this case, to be equal to the horizontal component of the pile capacity along the direction of batter. This method certainly requires more piles than necessary for a given condition and is not commonly used. 2. A commonly used method of analysis is known as Culmann’s graphical method, as shown in Figure 10.22. Piles are grouped according to their slopes. It assumes that all piles are subjected to axial load only and that piles in each group are subjected to equal axial load. Based on these assumptions, the center of reactions can be located. Culmann’s method may be described step by step as follows: a. Sketch a profile of the pile foundation and locate the center line of each group of parallel piles. b. Draw the resultant R of all external forces applied on the pile foundation. R intersects the center line of the pile group 1 (vertical piles) at point a. c. Center line of group 2 and center line of group 3 intersect at b. Connect ab. d. Resolve R into components V and B. V is vertical and B is parallel to line ab. e. Group 1 is subjected to total axial force V. Group 2 and Group 3 are subjected to force B. f. Resolve force B into axial loads along center line of group 2 and center line of group 3.

Figure 10.22

Graphical method (Culmann’s method). Column base plate.

This method is statically determinate where piles are arranged in not more than three directions; some examples are given by Teng (1964).

Design of Piles and Pile Groups

10.13

379

Design of Pile Foundations

The general criteria for the design of pile groups is that: 1. The load-carrying capacity of a single pile should not be exceeded due to loads and moments coming from the superstructure. 2. The load-carrying capacity of the group should not be exceeded by the total superposed loads. 3. The settlements, both total and differential, should be within permissible limits. The design of pile foundation may be carried out in the following steps: 1. Calculate the loads. The total load acting on the piles includes the weight of the pile cap and the soil above it. If the ground is newly filled or will be filled in the future, the additional load on piles due to negative skin friction should be included (Chapter 9). 2. Get the soil profile of the site and, superimpose the outline of the proposed foundation and substructure on this. Mark the ground water level. 3. Determine type and length of piles. 4. Determine pile capacity. 5. Establish pile spacing (Section 10.3). 6. Check stresses in lower strata (Section 10.8). These aspects are summarized below in terms of design guidelines.

10.14

Summary of Assumptions and Guidelines for Design

The details presented in the previous sections for pile foundation design are summarized for practical applications as follows: 1. Under a concentric load the piles are assumed to take equal axial loads in proportion to their areas of cross section (Section 10.5). 2. Under an eccentric loading or a concentric loading plus a moment, the pile group is designed with the following assumptions: a. Pile cap is rigid. b. Pile heads are hinged to the pile cap and therefore no bending moment is transmitted from the pile cap to the piles directly. c. Piles are short elastic columns. Therefore, the deformations and stress distribution are planar. d. The axial and lateral loads coming on any pile are calculated as explained in Section 10.5 (Equations (10.4)–(10.8)). 3. Uplift equal to the submerged self weight of the pile can be allowed. Where the uplift is due to load, including wind load, an additional resistance due to skin friction can be allowed. 4. When the pile is close to a deep foundation, skin friction should be neglected. 5. The following loadings on the pile need to be considered: a. Loads as supplied by the shop/structural requirements. b. Full weight of the pile cap. c. Submerged weight of pile cap.

Foundation Design

380

d. Full weight of soil above pile cap. e. Submerged weight of soil above pile cap. f. A surcharge on the gross area of the pile cap. 6. Combination of loads. a. The combination of loading for a maximum compressive load is a þ b þ d þ f þ maximum bending moment at the CG of the pile group due to Px ; Py ; Pz The combination of loading for a minimum compressive or maximum tensile load is a þ c þ e þ minimum bending moment at the CG of the pile group due to Px ; Py ; Pz b. The bending moment at the CG of the pile group is Moment due to Px or Py ; i:e: ; My ¼ Px h M x ¼ Py h

ð10:32Þ ð10:33Þ

where h is the thickness of the pile cap. c. Torsional moments on the pile group: These are caused due to eccentricity of horizontal loads acting at the center line of the column and also due to eccentricity of the horizontal loads acting on the whole structure, For example Mz ¼ Px ey þ Py ex þ Mzc

7.

8. 9. 10.

ð10:34Þ

where ex and ey are eccentricities of the center line of the column with respect to CG of the pile group along x and y directions. Mzc is the torsional moment transmitted by the columns of the structure. Pile groups in some cases have to be made eccentric with respect to the module axis (axes passing through C.G of the columns) to reduce the effect of overturning moment, keeping in view that this eccentricity deos not cause any adverse effect in any case of loadings, including reversal of direction of moment. When there is an increase of moment due to eccentricity, it has to be taken into account. Torsional moment Mz is shared in proportion to the torsional stiffness Izz/L of the pile where Izz is the polar moment of inertia and L is the length of pile. Minimum center to center spacing between piles is taken as 2.5D to 3.0D where D is the diameter of the pile. Clearances from the edge of pile cap to the various members are as follows: Piles Base plate Center of anchor bolts

15 cm 15 cm 35 cm

Depth of pile cap is taken as equal to the maximum length of anchor bolts in concrete with a cover of 0.25 m. 11. Bending moment in the i-th pile, Mbi due to horizontal force is calculated as Mbi ¼ Phi

Lfi 2

ð10:35Þ

Design of Piles and Pile Groups

381

where Phi is the total horizontal force coming on the i th pile (Equation 10.8), Lfi is the fixity length of i th pile (Section 10.5.4). This is an empirical/approximate method based on some design practices, as discussed in Sections 9.7 and 10.6. This needs to be verified by local practices and codes as well as by other methods discussed in Sections 9.7 and 10.6. As per the design practice, only the pile reinforcement is computed using BM due to lateral load and the vertical load on a pile as in a RCC column. 12. Maximum allowable stresses in steel and concrete are increased by 33% when that increase is due to wind load only. Usually Mbi is obtained by analysis of pile subjected to lateral loads or by pile load tests (Section 10.6). However to make the computation simple, Mbi may be calculated using Equation (10.35). The fixity length Lf can be taken from the graphs given in Figure 10.6 (IS: 2911–1984, 1984). In the absence of any data, it may be assumed to be around 5d to 10d where d is the diameter of the pile. 13. Batter piles: when excessive horizontal forces are encountered, batter piles could be used. 14. The axial loads and horizontal loads coming on a pile in a group are calculated using Equation (10.4) (Section 10.5).

10.15

Example

An example of the analysis and design of pile foundations is given below which essentially highlights the important steps involved, the use of specifications and assumptions and simplified approach to practical problems.

Example 10.1 Design a pile foundation with the following data. The details of column base plate and the pile group are shown in Figures 10.23 and 10.24. Loads coming from the column to the pile group are: Pz ¼ 1663 kN; Py ¼ 0; Mx ¼ 0; Px ¼ ðwind ¼ 60:62 kN; crane ¼ 64:90 kNÞ; My ¼ ðwind ¼ 1036:8 kNm; due to loads ¼ 1579:8 kNmÞ where Px, Py, Pz are the loads along the x, y, z axes. Mx, My, Mz are the moments about the x, y, z axes coming from the column (superstructure). The loads and moments are considered positive if they are acting along and about the positive direction of the respective axes as per usual convention.

10.15.1 Type A

10.15.2

Types of Piles Diameter (m)

Capacity (kN)

3d spacing (m)

0.50

1200

1.5

Concrete Data Unit weight of concrete ¼ 24 kN=m3 Submerged unit weight of concrete ¼ 14 kN=m3

Foundation Design

382

Figure 10.23

Column base plate.

Figure 10.24

Pile group.

Design of Piles and Pile Groups

10.15.3

383

Soil Data

The soil is uniform with the following data: Cohesion; c ¼ 14 kN=m3 Angle of internal friction; f ¼ 340 Bulk unit weight ¼ gt ¼ 17:5 kN=m3 Submerged unit weight ¼ gsub ¼ 10 kN=m3

10.15.4

Loads From the Superstructure Px ¼ 1663 kN Px ¼ 60:62 kNðwindÞ þ 64:90 kNðcraneÞ ¼ 125:2 kN My ¼ 1036:8 kNm ðwindÞ þ 1579:8 kNm ðloadÞ ¼ 2616:6 2617 kNm Py ¼ 0; Mx ¼ 0 Surcharge ¼ 50 kN=m2

Let us assume that there is no eccentricity between the module axis (column center line) and the pile group. Let us try a group of four piles.

10.15.5

Modulus of Piles About the Axes Passing Through the CG of the Pile Group

Neglecting the moment of inertia of piles about their own centroidal axes passing through the center of gravity, the moments of inertia of the pile group can be written by parallel axis theorem as follows: About y axis; Iyy ¼ ð4 1:252 Þ A ¼ 6:25 A About x axis; Ixx ¼ ð4 0:752 Þ A ¼ 2:25 A About z axis; Izz ¼ 8:50 A where A is the area of the pile. Modulus of extreme piles: fy ¼

xA 1:25 yA 0:75 ¼ ¼ ¼ 0:2; fx ¼ ¼ 0:33 Iyy ð4 1:252 Þ Ixx ð4 0:752 Þ

Approximate size of pile cap ¼ð2:5 þ 0:5 þ 0:3Þ ð1:5 þ 0:5 þ 0:3Þ ¼ 3:3 m 2:3 m. Take 0.75 m to be the depth of the pile cap (area ¼ 3:3 2:3 ¼ 7:6 m2 ) as shown in Figure 10.24.

10.15.6

Loads

1. Column load ¼ 1663 kN. 2. Self weight of pile cap ¼ 3:3 2:3 24 0:75 ¼ 137 kN.

Foundation Design

384

3. Submerged weight pile cap ¼ 3:3 2:3 14 0:75 ¼ 80 kN. Assume the top of the pile cap to be 1 m below ground level. 4. Soil weight (1 m thick) ¼ 3:3 2:3 1:0 17:5 ¼133 kN. 5. Submerged weight of soil ¼ 3:3 2:3 1:0 10 ¼ 76 kN. 6. Surcharge (including floor weight if any) ¼3:3 2:3 50 ¼ 380 kN.

10.15.7 1. 2. 3. 4.

Moments

Data ¼ 2617 kNm. Data (without wind) ¼ 1580 kNm. Moment due to horizontal load ¼ 125:2 0:75 ¼ 94 kNm. Moment due to horizontal load (without wind) ¼ 64:9 0:75 ¼ 49 kNm.

10.15.8

Combination of Loads and Moments for Maximum Load on Pile

10.15.8.1 Loads Using data listed in Section 10.15.6 ¼ item 1 þ item 2 þ item 4 þ item 6 ¼ 1663 þ 137 þ 133 þ 380 ¼ 2313 kN 10.15.8.2 Moments Using data listed in Section 10.15.7 ¼ item 1 þ item 3 ¼ 2617 97 ¼ 2711 kNm 10.15.8.3 Maximum Load on Piles ¼ 2313=4 þ 2711=5 ¼ 580 þ 540 ¼ 1120 kN 10.15.8.4 Minimum Load on Piles ¼ 580540 ¼ 40 kN The maximum allowable load with wind is 33.33% above 1200 kN (1600 kN). Hence, it is acceptable.

Design of Piles and Pile Groups

10.15.9

385

Combination of Loads and Moments for Minimum Load on Pile

10.15.9.1 Loads Using data listed in Section 10.15.6 ¼ item 1 þ item 3 þ item 5 ¼ 1663 þ 8 þ 76 ¼ 1819 kN 10.15.9.2 Moments Using data listed in Section 10.15.7 ¼ item 1 þ item 3 ¼ 2617 97 ¼ 2711 kNm 10.15.9.3 Minimum Load Per Pile ¼ 1819=42711=5 ¼ 455542 ¼ 87 kN (tension) Allowable tensile load on the pile ¼ Self weight of about 18 m long pile p ¼ 18 0:5082 24 þ skin friction 4 ¼ 87:5 kN þ skin friction > 87 kN ðtensionÞ Hence, it is acceptable.

10.15.10

Maximum Load on Pile Without Wind

10.15.10.1 Loads Using data listed in Section 10.15.6 ¼ item 1 þ item 2 þ item 4 þ item 6 ¼ 2313 kN 10.15.10.2 Moments ¼ 1580 49 ¼ 1629 kNm 10.15.10.3 Maximum Load Per Pile ¼ 2313=4 þ 1629=5 ¼ 910 kN < 1200 kN Hence, it is acceptable.

Foundation Design

386

10.15.11

Design of Reinforcement in Pile

The pile has to carry a vertical load of 1120 kN (with wind). Fixity length of pile is taken as 5d (2.50 m). Horizontal load per pile ¼ 125.2/4 ¼ 31.3 kN (about 3% of nominal allowable load). Hence, it is acceptable. Bending moment to be carried by pile ¼ 31:3 5d=2 ¼ 31:3 1:25 40 kNm: A proper percentage of reinforcement has to be used for a vertical load of 1120 kN and bending moment of 40 kNm.

10.15.12

Pile Cap

10.15.12.1 Longer Direction (x–Axis) BM at the face of the base plate ¼ 2 1120 1:25 (due to two piles at a distance of xc ¼ 1.25 m from the CG of pile group and CL of column) ¼ 2800 kNm Shear at the face of the base plate ¼ 2 1120 (due to two piles) ¼ 2240 kN Provide reinforcement, check the adequacy of depth for BM and check for shear and bond stress. 10.15.12.2 Shorter Direction (y–Axis) Loads on piles ¼ 1120 þ 40 ¼ 1160 kN (due to one pile with 1120 kN and second pile with 40 kN). Bending moment at the face of the base plate ¼ 1160 yc ¼ 1160 0:75 ¼ 870 kNm (yc for both the piles is 0.75 m from the CG of the group and CL of column). Shear at the face of the base plate ¼ 1160 kN. Provide reinforcement for the BM and check for shear and bond stress.

10.15.13

Check for Vertical Load Capacity of Pile

Pile parameters: L ¼ 18 m; h ¼ 0:75 m; D ¼ 0:5 m Soil parameters:

f ¼ 34 ; c ¼ 14 kN=m2 ; gsub ¼ 10 kN=m3 ; assume Ko ¼ lateral earth pressure coefficient at rest ¼ 1:0 End bearing for f ¼ 34 ; c ¼ 14 kN=m2 ; Nc ¼ 52:64; Nq ¼ 36:5; Ng ¼ 38:04: Pb ¼

pD2 1:3 CNc þ gDF Nq þ 0:3g D Ng 4

Design of Piles and Pile Groups

Pb ¼

387

pð0:5Þ2 ½ð1:3 14 52:64Þ þ ð10ð18 þ 0:75Þ36:5Þ 4 þ 0:3ð0:5Þ 10 38:04

Pb ¼ 1543 kN 10.15.13.1 Friction and Adhesion Shear strength of the mid depth of the pile (assuming adhesion factor of a ¼ 1:0) and taking Ko ¼ 1:0, that is, at L/2 (neglecting the additional effect due to h), L tan f s ¼ c þ Ko gsub 2 18 ¼ 14 þ 10 0:5774 2 ¼ 66 kN=m2 Pf ¼ pDLs ¼ p 0:5 18 66 Pf ¼ 1866 kN Total pile capacity ¼ Pb þ Pf ¼ 1543 þ 1866 ¼ 3409 kN Safe capacity of vertical load on pile with factor of safety ¼ 3 is 3409 ¼ 1136:4 kN > 1120 kN 3 Hence, it is safe.

10.16

Construction Guidelines

Noting that piles transfer loads from the superstructure by either end-bearing and/or by skin friction, they can be used at sites where the above load transfer mechanisms are possible in the subsoil. Construction of pile foundations require a judicious choice of piling system depending on soil conditions, loads coming from the superstructure and constraints of total and differential settlements besides special requirements. The installation of piles requires careful control on position, alignment, depth which involves skilled and experienced manpower. Pile load test (Section 9.6.7) is the most direct method to assess the above requirements and judging its performance. The details of testing are similar to the plate load test (Chapter 4) but instrumentation needs to be elaborate as described in standard text books such as Taylor (1964), Teng (1964), Terzaghi and Peck (1967) and Bowles (1996).

10.16.1

Construction Details

The construction of pile foundations involves two steps, namely construction of piles and the pile caps. The second step is a simple process similar to the construction of spread footings. Procedures and equipment required for installation of piles are described below. Driven piles are installed by a pile driving device known as a pile hammer. The hammer may be suspended from the boom of a crane, supported on a large frame called a pile driver or carried on a barge for construction in water. In all cases, the hammer is guided between two parallel

388

Foundation Design

steel members known as leads. The leads may be adjusted at various angles for driving vertical and batter piles. Usually the information concerning the pile driving should be kept in an orderly form. It should include the details of the hammer and accessories. The behavior of the pile during the entire period of driving should be observed. It is time to stop driving a timber pile when the following phenomena are observed: 1. The pile vibrates and springs near the ground surface. 2. The pile hammer bounces. 3. The pile head shows distress under moderate driving. Pile may be already damaged if the following behavior is noticed: 1. Penetration suddenly increases or becomes irregular, while the soil profile cannot account for it. 2. Pile suddenly changes direction. Cast in situ piles are provided by drilling a bore hole with or without casing using drilling equipment and then placing reinforcement and concrete in the drilled bore hole (Section 9.2.2). 10.16.1.1 Alignment Piles cannot be driven (or cast in situ) absolutely vertical and true to position. Even in ideal conditions the center of a pile head must be allowed to deviate a certain amount from the required location, and the pile at lower depth to vary from the required vertical or batter line. However, every precaution should be exercised to maintain the piles in position. The general procedure for determining the pile alignment and elevations is as follows: 1. Measure the elevation at top of piles immediately after driving of each and check the final elevations after the adjacent piles are driven or at the completion of all pile driving. If pointbearing piles are uplifted, they should be redriven. 2. Check the location of all piles after adjacent piles are driven or at the completion of all pile driving. In ordinary soil conditions an 8 cm tolerance is considered reasonable. 3. Inspect the pile shaft for verticality or required batter. In the case of heavily loaded piles measurement must be made by specially devised instruments, unless load test is made with piles having questionable verticality. The above steps are equally applicable for cast-in-situ piles as well. 10.16.1.2 Defective Piles A pile may be considered defective if: 1. It is damaged by driving. 2. It is driven out of position and/or is bent along its length. To avoid damage to fresh concrete in a cast in place pile by the driving of adjacent piles, the pile should not be concreted until all piles within a certain radius are driven. The radius depends upon soil condition, length and size of pile and spacing.

Design of Piles and Pile Groups

389

A damaged or defective pile has to be withdrawn and replaced by another pile adjacent to it after checking the design with the new position of the replaced pile. Alternatively a new pile may be driven/cast while leaving the damaged pile as it is. 10.16.1.3 Effect of Pile Driving Pile driving may introduce some of the following effects on the ground: 1. Subsidence. Vibration due to pile driving in loose sand may cause compaction of the sand. Consequently, the area may settle and adjacent structures may be affected. In saturated fine sand and silt, the shock may introduce large settlements. 2. Heave. Pile driving in clays and dense sand is commonly associated with surface heave and sometimes with lateral displacement. The heave of clay is followed by settlement immediately after driving. Piles uplifted by ground heave should be redriven. To avoid heave and lateral movement, pile driving should be started from the center of the ground and proceed outwards. 3. Compaction. Sand and gravel within a lateral distance of about three diameters of the pile and two diameters below the tip is largely compacted due to the displacement of pile. Consequently, a pile group in sand behaves as a rigid block of compacted soil. 4. Disturbance. Clayey soil surrounding the pile is greatly disturbed due to the displacement of pile. The disturbance may extend to a large lateral distance and the strength of clay is largely reduced. However, in ordinary cases it starts to regain its strength and in 30–50 days; 90% or more of its strength may be regained.

Exercise Problems The problem assignments are mainly on pile foundation design, that is, Sections 10.13 and 10.14. Use concrete of grade M20 and steel of grade Fe450, unless stated otherwise. 10.1

10.2

10.3

10.4

10.5

Analyze a pile foundation with the following data. Pile diameter ¼ 0.6 m, number of piles ¼ 5. Soil data: c ¼ 15 kN=m2 , f ¼ 20 , g ¼ 17 kN=m3 . Depth of pile cap surface below GL ¼ 1 m. No ground water at site. Column size ¼ 0.6 0.6 m. Length of anchor bolt in the pile cap ¼ 0.4 m. Px ¼ 1000 kN, Py ¼ 500 kN, Pz ¼ 200 kN, Mx ¼ 1000 kNm, My ¼ 200 kNm, Mz ¼ 150 kNm, surcharge ¼ 50 kN/m2. Use five piles as shown in Figure 10.25 and find the length of pile required to get the required capacity with a Factor of safety ¼3. All specifications are to be satisfied. Design a pile foundation with a group of circular piles of 0.5 m diameter with the same data for soil, top of pile cap, column, loads and moments. Also find the length of pile required with a factor of safety ¼ 3. Calculate the elastic and consolidation settlements of the group (Problem 10.1 and Figure 10.25) if there is a compressible layer of 10 m thick clay from 20 to 30 m from ground level, mv of compressible soil ¼ 25 103 m2 =kN: Analyze the pile group given in Figure 10.25 if the piles are of different diameters. P1 and P2 ¼ 0.4 m diameter, P3 and P4 ¼ 0.6 m diameter, P5 ¼ 1.0 m diameter. Use the same data as given in Problem 10.1 except for the diameters of piles. Design the pile group of Problem 10.2 if the water table is at a depth of 5 m below GL.

Foundation Design

390

Figure 10.25

10.6

Problem 10.1.

For the pile group shown in Figure 10.26, find design loads and moments on each pile with the following data (loads in kN; moments in kNm): Pz ¼ 2250; Px ¼ 200; Py ¼ 150; Mx ¼ 3000; My ¼ 2000 Depth of pile cap ¼ 2 m Unit weight of concrete ¼ 24 kN/m2

Figure 10.26

Problem 10.6.

Design of Piles and Pile Groups

391

Depth of top surface of pile cap below GL ¼ 1.5 m Unit weight of soil ¼ 17.7 kN/m3 Surcharge ¼ 50 kN/m2 Fixity length of pile ¼ 6d (d is diameter of pile) Submerged unit weight of soil ¼ 10.5 kN/m3 Submerged unit weight of concrete ¼ 14 kN/m3 Diameters of piles 1 and 2 ¼ 0.5 m Diameters of piles 3 and 4 ¼ 0.75 m Water table can rise up to GL. 10.7

Compute the permissible lateral load for the offshore circular pile shown in Figure 10.27. If the maximum permissible lateral displacement is d/10 where d is the diameter of pile. Diameter of pile ¼ 0.5 m. Pile is quite long and can be analyzed as a semi-infinite beam on elastic foundation. Esoil ¼ 15 MPa, nsoil ¼ 0.2. Econcrete may be taken appropriately. Use BEF approach.

Figure 10.27

10.8

Problem 10.7.

Redo the example 10.7 with pile head at the ground level.